During their lifecycle, structures change their properties due to different reasons, for instance damage, corrosion or fatigue. With increasing maturity of sensor technology and numerical simulation techniques, it is possible to have a digital representation (Digital-Twin) of the complex structures. One of the most important steps in Digital-Twinning is the system identification, which involves identification of the current state of the material properties and/or localization of the weakening [1]. That requires to solve the inverse problem using suitable parameterization of the structure. Typically, this can be formulated as an optimization problem [1]. This work focuses on solving the minimization problem for identifying the material properties in the numerical model. The cost function formulation is based on the aggregated error between measured and computed displacements and strains in different locations. The work applies p-norm aggregation technique to better weight the contributions from different sensors. Additionally, different smoothing techniques and filtering, such as Vertex Morphing approach [2], is applied to regularize the minimization problem. In this work, we propose different optimization algorithms [3], which are reviewed and studied on a few different 2D and 3D representative structural problems and compared to a well-known base method, i.e. Steepest Descent with constant scaled step. [1] Airaudo, F.N., Löhner, R., Wüchner, R. and Antil, H., 2023. Adjoint-based determination of weaknesses in structures. Computer Methods in Applied Mechanics and Engineering, 417, p.116471. [2] Antonau, I., Warnakulasuriya, S., Bletzinger, KU. et al. Latest developments in node-based shape optimization using Vertex Morphing parameterization. Struct Multidisc Optim 65, 198 (2022). [3] Antonau, I., Enhanced computational design methods for large industrial node-based shape optimization problems. Dissertation. TUM School of Engineering and Design, Technische Universität München, 2023.